A population of bacteria is growing according to the equation P (t)=1100e^0.04t. Estimate when the population will exceed 1455.

Answer :

Solution:

[tex]p(t)=1100e^{0.04t}[/tex]

We want to estimate the population when the population exceed 1455

Set p(t) = 1455 and solve for t

[tex]\begin{gathered} 1100e^{0.04t}=1455 \\ Divide\text{ both sides by 1100} \\ \frac{1100e^{0.04t}}{1100}=\frac{1455}{1100} \\ \\ e^{0.04t}=1.322727 \\ lne^{0.04t}=ln1.322727 \\ 0.04t=0.27763 \\ t=\frac{0.27763}{0.04} \\ t=6.99 \end{gathered}[/tex]

Thus, the population will exceed 14551 after 6.99 years